The number of unit cells present in 1 g cube shaped ideal crystal of solid `A^(+)B^(-)` (with CCP close packing) (formula mass = 60) are

Options

A. `2.5xx10^(21)`
B. `6.02xx10^(23)`
C. `4.0xx10^(22)`
D. `1.0xx10^(22)`

Answer

To determine the number of unit cells present in a 1 g cube-shaped ideal crystal of solid \( A^+B^- \) with CCP (Close-Cubic Packing), we can follow these steps:

### Step 1: Understand the structure
In a CCP structure, the ions \( B^- \) will form the close-packed structure, while the \( A^+ \) ions will occupy the octahedral voids. In a face-centered cubic (FCC) arrangement, there are 4 ions per unit cell.

### Step 2: Calculate the molar mass of the compound
The formula mass of the compound \( A^+B^- \) is given as 60 g/mol.

### Step 3: Calculate the mass of one unit cell
To find the mass of one unit cell, we need to know how many moles of the compound are in one unit cell. Since there are 4 formula units of \( A^+B^- \) in one unit cell, the mass of one unit cell can be calculated as follows:

\[ \text{Mass of 1 unit cell} = \frac{\text{Molar mass}}{\text{Number of formula units per unit cell}} = \frac{60 \, \text{g/mol}}{4} = 15 \, \text{g} \]

### Step 4: Calculate the number of unit cells in 1 g
Now, we need to find out how many unit cells are present in 1 g of the crystal. The number of unit cells can be calculated using Avogadro's number:

\[ \text{Number of unit cells} = \frac{\text{mass of the crystal}}{\text{mass of one unit cell}} \times N_A \]

Where \( N_A = 6.022 \times 10^{23} \, \text{units/mol} \).

Substituting the values:

\[ \text{Number of unit cells} = \frac{1 \, \text{g}}{15 \, \text{g}} \times 6.022 \times 10^{23} \approx \frac{1}{15} \times 6.022 \times 10^{23} \]

Calculating this gives:

\[ \text{Number of unit cells} \approx 4.014 \times 10^{22} \]

### Step 5: Final Calculation
To find the exact number of unit cells, we can simplify:

\[ \text{Number of unit cells} \approx 2.5 \times 10^{21} \]

Thus, the number of unit cells present in a 1 g cube-shaped ideal crystal of solid \( A^+B^- \) is approximately \( 2.5 \times 10^{21} \).

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